Characterization and Modeling of Pedal Torque in a Regenerative Bicycle Trainer Using Current Control

Regenerative bicycle trainers support more sustainable indoor cycling by converting a rider’s kinetic energy into electrical energy while producing a controllable resistive load. For a realistic riding feel, the relationship between commanded braking current and pedal torque must be accurately defined. This study develops and validates an empirical current-torque model for a trainer based on a brushless direct current (BLDC) motor using a second-order polynomial. Experiments were conducted on two sprocket configurations (32-tooth and 12-tooth), with 11 braking current setpoints ranging from 0 to 10 A under steady-state conditions. The model was evaluated through its inverse form using five torque setpoints for each configuration. Results show strong agreement with experimental data, with coefficients of determination ( ) exceeding 0.998. The 12T configuration achieves higher accuracy, with a Mean Percentage Error of 1.55%, compared to 9.20% for the 32T configuration. This is likely due to improved torque transmission and more stable friction drive behaviour at higher loads. Negative quadratic coefficients indicate mild nonlinearities consistent with magnetic saturation. The model is suitable for feedforward control, enabling realistic torque simulation without requiring expensive external torque sensors.